Question

Does living together cause divorce? Couples were given a standardized psychological assessment that indicates the likelihood of divorce (higher scores indicate a higher likelihood of divorce) and asked them how many months they've lived together. The data is reported below:

Likelihood of divorce score	Months lived together
87	54
65	36
45	20
32	5
05	0

Please complete all steps of hypothesis testing, create a scatterplot, and write a short explanation for what you think may be the underlying factor in this correlation (hint: be careful not to associate causal factors).

Answer 1

We now have the following data:

Divorce	Lived
87	54
65	36
45	20
32	5
5	0

As such we get the higher scores indicates higher likelihood of divorce. In order to assess this, we shall calculate the correlation coefficient and then test it using testing of Hypothesis.

We calculate the correlation coefficient using the formula:

To calculate this quantity, we form the following table:

	87	54	7569	2916	4698
	65	36	4225	1296	2340
	45	20	2025	400	900
	32	5	1024	25	160
	5	0	25	0	0
Total	234	115	14868	4637	8098

We shall substitute the values into the formula:

We can see that the correlation coefficient is 0.9723. This indicates the linear relationship between likelihood of divorce and length of living together.

Null hypothesis: There is no correlation between likelihood of divorce score and months living together.

Alternate Hypothesis: There is a correlation.

Level of significance

Test statistic :   follows a t distribution with n-2 df.

The critical value of t at 3 df=3.1825 or the p-value is 0.0055. This can be found by T.INV.2T(0.05,3) function in EXCEL.

Since the calculated value of t>the critical value, we reject the null hypothesis and hence the correlation is present between likelihood of divorce score and months living together